Question: $\dfrac{ -3a - b }{ -5 } = \dfrac{ -10a - 8c }{ -7 }$ Solve for $a$.
Multiply both sides by the left denominator. $\dfrac{ -3a - b }{ -{5} } = \dfrac{ -10a - 8c }{ -7 }$ $-{5} \cdot \dfrac{ -3a - b }{ -{5} } = -{5} \cdot \dfrac{ -10a - 8c }{ -7 }$ $-3a - b = -{5} \cdot \dfrac { -10a - 8c }{ -7 }$ Multiply both sides by the right denominator. $-3a - b = -5 \cdot \dfrac{ -10a - 8c }{ -{7} }$ $-{7} \cdot \left( -3a - b \right) = -{7} \cdot -5 \cdot \dfrac{ -10a - 8c }{ -{7} }$ $-{7} \cdot \left( -3a - b \right) = -5 \cdot \left( -10a - 8c \right)$ Distribute both sides $-{7} \cdot \left( -3a - b \right) = -{5} \cdot \left( -10a - 8c \right)$ ${21}a + {7}b = {50}a + {40}c$ Combine $a$ terms on the left. ${21a} + 7b = {50a} + 40c$ $-{29a} + 7b = 40c$ Move the $b$ term to the right. $-29a + {7b} = 40c$ $-29a = 40c - {7b}$ Isolate $a$ by dividing both sides by its coefficient. $-{29}a = 40c - 7b$ $a = \dfrac{ 40c - 7b }{ -{29} }$ Swap signs so the denominator isn't negative. $a = \dfrac{ -{40}c + {7}b }{ {29} }$